A way to hide who makes purchases at a specific merchant?
Remember: silent payment hides the receiver. It's the merchant who gains the privacy. It's useful because it eliminates the burden of interactivity. Previously, the merchant needed a web server that continuously generated a whole new address for every visitor. Now, it's static, non-interactive; the burden has moved into the wallet software. The merchant still needs to be careful and not consolidate everything into one transaction, as it would harm their privacy.
Hiding the merchant ends up protecting both sides. Nobody knows where I spent that money.
My question now is: if the trader consolidates all these UTXO, will it be possible to identify who sent the money?
One large difference is that in Bitcoin, you can choose your own denomination. I've seen altcoins (BlackBytes) that have fixed denominations (like banknotes). In Bitcoin, unlike banknotes, your change is always one input.